What is (\partial)/(\partial x)(sqrt(6+3x^2-2y^2)) ?

The answer to (\partial)/(\partial x)(sqrt(6+3x^2-2y^2)) is (3x)/(sqrt(6+3x^2-2y^2))

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(\partial)/(\partial x)(sqrt(6+3x^2-2y^2))

\frac{\partial}{\partial x} (6 + 3 x^{2} - 2 y^{2})

\frac{3 x}{6 + 3 x ^{2} - 2 y ^{2}}

Solution steps

\frac{\partial}{\partial x} (6 + 3 x^{2} - 2 y^{2})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 6 + 3 x ^{2} - 2 y ^{2}} \frac{\partial}{\partial x} (6 + 3 x^{2} - 2 y^{2})

= \frac{1}{2 6 + 3 x ^{2} - 2 y ^{2}} \frac{\partial}{\partial x} (6 + 3 x^{2} - 2 y^{2})

\frac{\partial}{\partial x} (6 + 3 x^{2} - 2 y^{2}) = 6 x

= \frac{1}{2 6 + 3 x ^{2} - 2 y ^{2}} \cdot 6 x

Simplify

\frac{1}{2 6 + 3 x ^{2} - 2 y ^{2}} \cdot 6 x : \frac{3 x}{6 + 3 x ^{2} - 2 y ^{2}}

= \frac{3 x}{6 + 3 x ^{2} - 2 y ^{2}}

\int 4 x^{2} + \frac{1}{( 2 x ) ^{2}} d x

2 t^{4}

x \frac{d y}{d x} = y + 2 x e^{- \frac{y}{x}}

\frac{6 s}{( s ^{2} - 8 s + 25 )}

\int \frac{6}{x ln ( 7 x )} d x

What is (\partial)/(\partial x)(sqrt(6+3x^2-2y^2)) ?
The answer to (\partial)/(\partial x)(sqrt(6+3x^2-2y^2)) is (3x)/(sqrt(6+3x^2-2y^2))